7  Strategy ”always monopoly price” is not in equilibrium”Grim Strategy” (GS):Choose pi1= pMChoose pit= pM if pjt-1= pMElse always choose pit= 0Suppose j knows i plays GS; what is best for j?GS is best reply (among others) GS is a best reply against itself Both firms using GS is an equilibriumPunishment needs to be credible, otherwise it is only empty threatThere must be incentives to start punishmentPunishment must be part of equilibrium path from that moment onward, so that no firm will want to deviate from punishmentOne-shot Nash equil behavior always credible punishment3. Cartels and Collusion

9 "Folk Therorem": Any outcome that leaves each player more than one-shot minmax is sustainable as an equil outcome in infinitely repeated gameThere are many equilibrium strategies"Anything" is in equilNo predictive power w/o more assumptionsGenerally collusion is sustainable if temptation to defect is low enough and punisment following the deviation strong enoughFirm wants to keep colluding if present value of devi-ating is smaller than present value of adhering to collusive agreementPV of collusion here ViC = ttit(piC,pjC) = piC/(1-) as t dt = 1/(1-d) if |d| < 13. Cartels and Collusion

10 PV of deviation = profits reaped during deviation + present value of profits earned during punishment: ViD = D + ttit(piP,pjP) = D +  piP/(1-)Note: here punishment assumed to be infinitely longCollusion is sustainable ifIncentive to deviate depends on discount factorIf discount factor is too low to support collusion, either toughen up punishment or try to lower degree of collusionLonger or harder price warReduce collusive prices from monopoly priceNote: punisments are never observedNone used since threat is enough3. Cartels and Collusion

12 3. Cartels and Collusion Collusion with Imperfect InformationWhat if firms cannot observe rivals' exact prices nor quantities sold? Don't know if rival defected  don't know when to start price warNo threat of price war  collusion not sustainable?Use other info: Sales were less than expectedThink Bertrand oligopoly with identical goods and with stochastic demandFirm has 0 demand today: somebody deviated and stole customers or shift in demand?Start price war when price or demand drops "enough"Start price war even if you know nobody deviated, as nobody has incentives to deviateIntuition: no punishment  no firm has incentives to collude  per period equil only possibility3. Cartels and Collusion

13 3. Cartels and Collusion Factors that Help CollusionGeneral idea: stronger, earlier and more certain punishment increases possibilities to collusion”Topsy-Turvy” principle: the more firms have opportunities for aggressive competition, the less competition there isPublic prices and other market transparencyEasy to observe deviationSize of cartelN equally sized firmsEach firm receives 1/Nth share of total monopoly profitsCollusion sustainable if one shot defection followed by punishment leaves less profits that staying on collusive path:3. Cartels and Collusion

14 3. Cartels and Collusion Product differentation works two waysMore products are differentiated, the larger price decrease needed tosteal mkt sharepunish deviatorMore products are differentiated, less incentive to cheat and try to steal mkt shareMore products are differentiated, less price war by rivals affects profitsIntroduces non-price competition: more variables to monitor and more ways to cheatCost conditions and capacity utilizationCapacity constraint or steeply rising MC reduce profit margin for extra outputReduce incentive to cheatReduces possibilities and incentives to punish3. Cartels and Collusion

15 3. Cartels and Collusion Free capacity Increases temptation to cheatAllows harsher punishment  increases possibilities and incentives to punishElasticity of firm demandInelastic firm demand  more mkt share means significant reduction in price  less incentive to cheatMore elastic demand is, the harder it is to sustain collusionMultimarket contactFirms produce several competing goods or operate on several geographic mktsMore opportunities to cheatPrice war on all mkts  allows more severe punishments3. Cartels and Collusion

16 3. Cartels and Collusion Firm symmetryFirms have different shares of a specific asset (capital) which affects marginal costsJoint profit maximization: output is shifted away from small (inefficient) firms towards large (efficient) firmsSmallest firm has highest potential to steal business of its rivals and, has highest incentives to disrupt collusive agreementIncentives to deviate are reversed when equilibrium calls for punishmentsLargest firm loses most at punishment phase, it will have highest incentives to deviate from punishmentCapacity constraintsIncentives to stay in collusive equilibrium are very different for large and small firmsSmall firm will have some incentive to cheat in short run, as it can only increase its sales marginally up to capacity level3. Cartels and Collusion

17 Large firm has a lot more capacity available and can gain more customers with same price deviation from collusive normLarge firms tend to have a greater incentive to deviate from collusive priceAsymmetry in capacities will also have an important effect on effective punishmentsWorst punishment firm can impose on its competitors is to produce up to full capacitySmall firm that is already producing at almost full capacity has low possibilities to punish rivals that do not follow collusive normLarge firm competing with small firm will have large incentives to deviate from any collusive norm without this being disciplined threat of low prices in futureIncreases in asymmetries in capacities make collusion more difficult3. Cartels and Collusion

18 3. Cartels and Collusion Collusion and AntitrustSee Motta Ch 4, Europe Economics report, UPM/Haindl and Gencor/Lonrho decisions, and browse my ”forest” paperJoint dominance and coordinated effects in legal jargon ~ collusion in econ jargonCore of policy problem: Collusion arises as equilibrium behaviorHard to prohibit or deal with ex postSolution: try to prevent collusion, ban business practices and mergers that help to facilitate collusion – see aboveAnalyses of asymmetry in assets and capacity constraints suggest merger guidelines that differ from traditional wisdomFor a given number of firms, Herfindahl and other concentration tests predict that more symmetric industry is more competitive3. Cartels and Collusion

19 3. Cartels and Collusion Asymmetry may be pro-competitiveAsymmetric industry may even more than compensate for reduction in number of firms in merger involving large firmIncreased asymmetry hurts collusion and may benefit competitionHow to identify collusion?Possible to detect collusion from behavior alone?Firms have more mkt power than one shot equil?Estimate cost, demands and reaction fns and compare actual behavior to non-cooperative and collusive equilDoable, but gets technical with differentiated products (see Nevo, Slade)3. Cartels and Collusion